Let's analyze the problem step-by-step.
Problem Summary:
- A trader owes a merchant Rs. 10,028 due 1 year from now.
- The trader wants to settle the account after 3 months (i.e., 9 months before the due date).
- The rate of interest is 1% per annum.
- We need to find how much cash the trader should pay now (after 3 months) to settle the account.
Key Concept:
Since the payment is due after 1 year, but the trader wants to pay after 3 months, the amount should be discounted for the remaining 9 months at the given interest rate.
Step 1: Identify the variables
- Future value (FV) = Rs. 10,028 (amount due after 1 year)
- Rate of interest (r) = 1% per annum = 0.01
- Time difference (t) = 9 months = 9/12 = 0.75 years
Step 2: Calculate the present value (PV) after 3 months
Using the formula for present value with simple interest:
PV=FV1+r×tPV=\frac{FV}{1+r\times t}PV=1+r×tFV
Substitute the values:
PV=10,0281+0.01×0.75=10,0281+0.0075=10,0281.0075PV=\frac{10,028}{1+0.01\times 0.75}=\frac{10,028}{1+0.0075}=\frac{10,028}{1.0075}PV=1+0.01×0.7510,028=1+0.007510,028=1.007510,028
PV≈9,954.41PV\approx 9,954.41PV≈9,954.41
Final Answer:
The trader should pay Rs. 9,954.41 after 3 months to settle the account. If you want me to explain with compound interest or any other method, feel free to ask!
